SOLUTION: help me factor completely: 3a^3b^3-6a^2b^2-3ab

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Question 232490: help me factor completely: 3a^3b^3-6a^2b^2-3ab
Answer by jsmallt9(3758) About Me  (Show Source):
You can put this solution on YOUR website!
3a%5E3b%5E3-6a%5E2b%5E2-3ab
Always start factoring by factoring out the Greatest Common Factor (GCF), unless it is 1. The GCF here is 3ab:
3ab%28a%5E2b%5E2+-2ab+-+1%29
After the GCF you try any and all other factoring techniques, possibly repeatedly, until you can factor no more. But, after trying all the other factoring techniques, we find that this will not factor any further.

However, if the last term had been +3ab and not -3ab, then we would have:
3ab%28a%5E2b%5E2+-2ab+%2B+1%29
which does factor further. The second factor fits one of the factoring patterns, p%5E2+-+2pq+%2B+q%5E2+=+%28p-q%29%28p-q%29+=+%28p-q%29%5E2, with "ab" as "p" and "1" as "q". So our revised expression factors into
3ab%28ab-1%29%5E2